IE 486 Work Analysis & Design II
Instructor: Vincent Duffy, Ph.D.
Associate Professor of IE
Lab 2 Tutorial – Uncertainty in Decision Making
Fri. Feb. 2, 2006
Today – IE 486 Lab 2 tutorial
Discussion on uncertainty in decision making –
related to economic decision making and
material from ch.7 in Wickens on Decision
making in the context of human factors and
ergonomics.
In lab exercise: Suppose the range of outcomes is known, but
the probability distribution is unknown (uncertain). Use a sheet of
paper to illustrate the selection of alternative A, B or C based on four
different analytical criteria known as Maxi-min, Maxi-max, Mini-max
regret, and equal likelihood. Write the payoff matrix on your sheet of
paper and re-calculate to decide based on each of the four criteria.
Lab 2 Exercise: Decision Making & Uncertainty.
Suppose the range of outcomes is known, but the probability distribution is
unknown (uncertain). Use a sheet of paper to illustrate the selection of
alternative A, B or C based on four different analytical criteria known as Maximin, Maxi-max, Mini-max regret, and equal likelihood. Write the payoff matrix on
your sheet of paper and re-calculate to decide based on each of the four criteria.
Observed outcomes of four trials are shown in the payoff matrix below.
For each method, determine the expected outcomes before making your
decision.
What is illustrated by the use of the different analytical techniques?
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
1. Maxi-min criteria - pessimistic view
try to maximize the minimum outcome
a. for any given alternative (eg. A,B, or C), assume the worst possible outcome.
b. choose the best (of those previously chosen).
2. Maxi-max criteria - optimistic view
try to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume the best possible outcome.
b. choose the best (of those previously chosen).
3. Mini-max regret criteria
–
–
Mini-max Regret: minimize the maximum possible regret.
regret: difference between observed and best payoff.
4. Equal-likelihood criteria
a. for any given alternative (eg. A,B, or C), assume all outcomes are equally likely.
b. maximize the expected value.
Analytical tools for decision making
under uncertainty
from Chapter 4 in Babcock in Managing Engineering and
Technology (Babcock, 1991).
– especially...
Decision making under uncertainty. p. 74-75 (today)
– In Babcock, D.L. 1991. Managing engineering and technology: an
introduction to management for engineers, Prentice-Hall:
Englewood Cliffs, NJ.
You may consider ‘economic’ decision making (related to
decisions made on investment alternatives) somewhat
different from ‘cognitive’ considerations in decision making
(related to decisions made during a task) from the Wickens
text.
However, this material may be considered to help bridge
the material without considering ‘time value of money’ yet.
Uncertainty - example 1
In a discussion of forecasting, and decision
making
– Suppose the range of outcomes is known, but
the probability distribution is unknown
(uncertain).
1. Maxi-min criteria - pessimistic view
– try to maximize the minimum outcome
– a. for any given alternative (eg. A,B, or C), assume the worst
possible outcome.
– b. choose the best (of those previously chosen).
Uncertainty - example 1
In a discussion of forecasting, and decision making
Suppose the range of outcomes is known, but the probability
distribution is unknown (uncertain).
1. Maxi-min criteria - pessimistic view
try to maximize the minimum outcome
a. for any given alternative (eg. A,B, or C), assume the worst
possible outcome.
b. choose the best (of those previously chosen).
Example 1) Suppose we have the following payoff matrix
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
Uncertainty - example 1
In a discussion of forecasting, and decision making
Suppose the range of outcomes is known, but the probability
distribution is unknown (uncertain).
1. Maxi-min criteria - pessimistic view
try to maximize the minimum outcome
a. for any given alternative (eg. A,B, or C), assume the worst
possible outcome.
b. choose the best (of those previously chosen).
Example 1) Suppose we have the following payoff matrix
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
0
Uncertainty - example 1
1. Maxi-min criteria - pessimistic view
try to maximize the minimum outcome
a. for any given alternative (eg. A,B, or C), assume the worst
possible outcome.
b. choose the best (of those previously chosen).
Example 1) Suppose we have the following payoff matrix
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
0
1
Uncertainty - example 1
1. Maxi-min criteria - pessimistic view
try to maximize the minimum outcome
a. for any given alternative (eg. A,B, or C), assume the worst
possible outcome.
b. choose the best (of those previously chosen).
Example 1) Suppose we have the following payoff matrix
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
0
1
0
for maxi-min criteria: choose B
Uncertainty - example 2
2. Maxi-max criteria - optimistic view
try to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume
the best possible outcome.
b. choose the best (of those previously chosen).
Uncertainty - example 2
2. Maxi-max criteria - optimistic view
try to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume the
best possible outcome.
b. choose the best (of those previously chosen).
Example 2) Suppose we have the following payoff matrix
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
Uncertainty - example 2
2. Maxi-max criteria - optimistic view
try to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume the
best possible outcome.
b. choose the best (of those previously chosen).
Example 2) Suppose we have the following payoff matrix
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
6
Uncertainty - example 2
2. Maxi-max criteria - optimistic view
try to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume the
best possible outcome.
b. choose the best (of those previously chosen).
Example 2) Suppose we have the following payoff matrix
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
6
4
Uncertainty - example 2
2. Maxi-max criteria - optimistic view
try to maximize the maximum outcome
a. for any given alternative (eg. A,B, or C), assume the
best possible outcome.
b. choose the best (of those previously chosen).
Example 2) Suppose we have the following payoff matrix
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
6
4
8
for maxi-max criteria: choose C
Uncertainty - example 3
3. Mini-max regret criteria
– Mini-max Regret: minimize the maximum possible
regret.
– regret: difference between observed and best payoff.
eg. suppose we chose B, but in outcome 1, if we had
chosen A we could have had 6 (from A) instead of 2 (from
B).
So we have regret…if only we had chosen A, we could
have had 4 more!
Uncertainty - example 3
3. Mini-max regret criteria
Mini-max Regret: minimize the maximum possible regret.
regret: difference between observed and best payoff.
Example 3) Suppose we have a payoff matrix (payoff)
observed outcome
(regret matrix) observed outcome
alternative___1___2___3___4____ _______ _1 2 3 4___max___
A
6
0
1
3
A
B
2
4
4
1
B
C
0
1
3
8
C
for mini-max regret criteria: *choose A
Uncertainty - example 3
3. Mini-max regret criteria
eg. suppose we chose B, but in outcome 1, if we had chosen
A we could have had 6 (from A) instead of 2 (from B). So we
have regret…if only we had chosen A, we could have had 4
more!
Example 3) Suppose we have a payoff matrix (payoff)
observed outcome
(regret matrix) observed outcome
alternative___1___2___3___4____ ______ _ _1 2 3 4___max___
A
6
0
1
3
A
0
B
2
4
4
1
B
4
C
0
1
3
8
C
6
Uncertainty - example 3
3. Mini-max regret criteria
eg. suppose we chose B, but in outcome 1, if we had chosen
A we could have had 6 (from A) instead of 2 (from B). So we
have regret…if only we had chosen A, we could have had 4
more!
Example 3) Suppose we have a payoff matrix (payoff)
observed outcome
(regret matrix) observed outcome
alternative___1___2___3___4____ ______ _ _1 2 3 4___max___
A
6
0
1
3
A
0
B
2
4
4
1
B
4
C
0
1
3
8
C
6
Uncertainty - example 3
3. Mini-max regret criteria
Example 3) Suppose we have a payoff matrix (payoff)
observed outcome
(regret matrix)
alternative___1___2___3___4__________
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
observed outcome
_ _1 2 3 4___max___
A
0 4
B
4 0
C
6 3
Uncertainty - example 3
3. Mini-max regret criteria
Example 3) Suppose we have a payoff matrix (payoff)
observed outcome
(regret matrix) observed outcome
alternative___1___2___3___4____ __________ _1 2 3 4___max___
A
6
0
1
3
A
0 4 3
B
2
4
4
1
B
4 0 0
C
0
1
3
8
C
6 3 1
Uncertainty - example 3
3. Mini-max regret criteria
Example 3) Suppose we have a payoff matrix (payoff)
observed outcome
(regret matrix) observed outcome
alternative___1___2___3___4____ __________ __1 2 3 4___max___
A
6
0
1
3
A
0 4 3 5
5
B
2
4
4
1
B
4 0 0 7
7
C
0
1
3
8
C
6 3 1 0
6
for mini-max regret criteria: choose A
Uncertainty - example 4
4. Equal-likelihood criteria
– this looks more like a ‘risk’ problem because you
do use ‘assumed’ probabilities
a. for any given alternative (eg. A,B, or C),
assume all outcomes are equally likely.
b. maximize the expected value.
Uncertainty - example 4
4. Equal-likelihood criteria
a. for any given alternative (eg. A,B, or C), assume all
outcomes are equally likely.
b. maximize the expected value.
Example 4) Suppose we have the following payoff matrix
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
(6+0+1+3)/4 = 10/4
Uncertainty - example 4
4. Equal-likelihood criteria
Example 4) Suppose we have the following payoff matrix
observed outcome
alternative___1___2___3___4____
A
6
0
1
3
B
2
4
4
1
C
0
1
3
8
expected
outcome ______
(6+0+1+3)/4 = 10/4
(2+4+4+1)/4 = 11/4
(0+1+3+8)/4 = 12/4
for maxi-max criteria: choose C